The species and idempotents of the Green algebra of a finite group with a cyclic Sylow subgroup

We study the Green algebra A(kG) generated by the isomorphism classes of indecomposable kG-modules, where k is a field with chark=p>0 and G a finite group with a cyclic Sylow p-subgroup. More precisely, we discuss the homomorphisms A(kG)→C (called species) and state a formula for the idempotents of A(kG).